Jacobi forms and a two-variable $p$-adic $L$-function

A construction which associates a $p$-adic family of modular forms with a Jacobi form is presented in the paper. The construction comes from the consideration of certain differential operators related with the Taylor expansion of Jacobi forms. As an application, a two-variable $p$-adic $L$-function connected with the special values of symmetric square is constructed.